Ronald Reagan began his presidency yesterday on a dramatic high note as he moved from ceremony to ceremony to the cheers of friendly crowds against the background of the successful end to the 14 1/2-month hostage crisis.

From the moment Reagan awoke on his inauguration day, he was caught up in events moving to make this a day Washington and the nation would long remember. The words said were less memorable than the bouyant images of a president taking command with easy assurance and seemingly in control of even the weather.

The hostage release, he said, made the entire day perfect.

It was 5:15 p.m. and the ceremonies were over before Reagan spent any significant amount of time inside his new home, the White House, but even prior to setting foot in the Oval Office as president, he seemingly was well in charge and riding a winning streak.

His first executive action, an order freezing federal civilian hiring, was almost lost in the inaugural and hostage-related events.

Reagan's order fulfilled a campaign pledge, and the president said "this begins the process of revising and reducing the 1981 and 1982 budgets, project that will occupy much of our time during the coming weeks and months."

The national budget, Reagan said, "is out of control." Aides said the freeze differs from the existing one because it applies to all employees, not just full-time, permanent workers, and it is total rather than allowing one person to be hired for every two who leave the government.

The highest level government jobs are exempt from the freeze.

Reagan awoke at 7:30 a.m. after having stayed awake late to watch the televised replay of Monday night's Capital Centre gala and to read several newspapers, press secretary James Brady said.

He was greeted by a sunny morning with the temperature headed into the 50s for the outdoor inauguration and parade.

At 8:31 a.m., President Carter telephoned Reagan at Blair House to inform him that the hostage snag had been overcome and the release of the 52 Americans appeared imminent.

Still, as Reagan dressed and with his wife, Nancy, packed the two suitcases they were taking immediately to the White House, there was no further good news. The delay continued as Reagan, described by Brady as being in a more "subdued" mood yesterday morning after being "sky high" Monday night, drove to St. John's Church on Lafayette Square with members of his family and his closest aides.

After returning to Blair House, the Reagans left at 10:33 a.m. for the traditional "inaugural coffee" at the White House with the outgoing president.

As a result of the continuing delay, Reagan knew the hostages were aboard Algerian airliners on the runway at Tehran as he heard himself announced as "the president-elect" for the last time and stepped onto the sunny platform at the West Front of the Capitol to take the oath of office.

"I, Ronald Reagan, do solemnly swear . . .," he began, repeating the words, after Chief Justice Warren Burger. Reagan's left hand rested on a family Bible used and annotated by his mother.

Reagan's voice was clear and confident as he launched into his 20-minute inaugural address, which he had written on nine sheets from a yellow legal pad after consultation and research with several aides, primarily Ken Khachigian, one of his principal speechwriters.

Reagan appealed for a revival of the American spirit to lead the country to new levels of greatness.

"We are too great a nation to limit ourselves to small dreams," he said.

He recited a list of battlefields where Americans have died from World War I through Vietnam, but said that the sacrifice Americans must make today is different, requiring "our best effort and our willingness to believe in ourselves and in our capacity to perform great deeds; to believe that together with God's help we can and will resolve the problems which confront us."

About 12:35 p.m., as the new president stood surrounded by close aides and family, his press secretary tapped him on the shoulder and whispered that the first plane had taken off from Tehran. Brady said he got the news by telephone from the White House situation room.

Minutes later, with word that the second plane was airborne, Reagan remained cautious, according to Brady. "Wait until they've cleared Iranian airspace so we can take that last little deep breath," the president said.

Reagan proceeded into the President's Room at the Capitol where he signed the nominations of his Cabinet officers and the hiring freeze order. Then he walked to Statuary Hall for lunch with members of Congress, the Supreme Court and their spouses.

In his luncheon toast, after speaking of the unity exemplified by the presence of the president, members of both houses of Congress and California wine, Reagan grew more serious:

"And now, to conclude the toast, with thanks to almighty God, I have been given a tag line, the get-off line that everyone wants for the end of a toast or a speech or anything else. Some 30 minutes ago the planes bearing our prisoners left Iranian airspace and now are free of Iran.

"So we can all drink to this one -- to all of us together, doing what we all know we can do to make this country what it should be, what it can be, what it always has been."

After watching the inaugural parade, Reagan sat for the first time behind his desk in the Oval Office and posed for photographers. Reagan said of the hostage release: "It makes the whole day perfect."

Then he added a joke: "I guess I can go back to California now."

Although Reagan had fallen more than 30 minutes behind schedule by the time he left the Capitol to ride in his limousine at the head of the inaugural parade, the car moved at a walking pace so that the new president and his wife, standing up through the sunroof, could wave, see and be seen the length of Pennsylvania Avenue. They ducked inside only once, when the car passed some demonstrators outside the FBI building.

Reagan loved it. He grinned and pointed to things that caught his attention.

Reagan titled the autobiography he wrote at the end of his acting and the start of his political career "Where's the Rest of Me?"

One aide suggested to him during the campaign that if he writes another, he might use as the title the sentence crowds like yesterday's shout as he drives past: "There He Is."